Properties

Label 2.25.aq_eh
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $1 - 16 x + 111 x^{2} - 400 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0738526172967$, $\pm0.28436638136$
Angle rank:  $2$ (numerical)
Number field:  4.0.46224.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 321 370113 244628964 152738602953 95357916129201 59598685407459600 37252000554119507841 23283020479166964777993 14551925357892480474958884 9094949928966083773271598753

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 592 15658 391012 9764650 244116214 6103367770 152587603012 3814699921018 95367462167152

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.